Answer:
centre = (9, 7 )
Explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
use the method of completing the square to obtain standard form
given
x² + y² - 18x - 14y + 124 = 0
collect the x/ y terms and subtract 124 from both sides
x² - 18x + y² - 14y = - 124
to complete the square
add ( half the coefficient of the x/y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 7)y + 49 = - 124 + 81 + 49
(x - 9)² + (y - 7)² = 6 ← in standard form
with centre = (h, k ) = ( 9, 7 )